Finite Group Databasebeta

← C11×#2462 #13065300

Subgroups — C11×#2462 #13065300

Order 1408.

452 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#125C211yesmaximal, characteristic
2C2×C4×Q8×C11C211yesmaximal, characteristic
3C11×#398C211yesmaximal, characteristic
4C11×#398C211yesmaximal, characteristic
5C11×#395C211yesmaximal, characteristic
6C11×#395C211yesmaximal, characteristic
7C11×#389C211yesmaximal, characteristic
8C11×#389C211yesmaximal, characteristic
9C11×#387C211yesmaximal, characteristic
10C11×#387C211yesmaximal, characteristic
11C11×#387C211yesmaximal, characteristic
12C11×#387C211yesmaximal, characteristic
13C11×#387C211yesmaximal, characteristic
14C11×#387C211yesmaximal, characteristic
15C4×C11×C4⋊C4C211yesmaximal, characteristic
16C22×Q8×C11C2211yescharacteristic
17C11×#125—24no—
18C4×Q8×C11—24no—
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C4⋊C4C2211yescharacteristic
24C2×C11×C4⋊C4C2211yescharacteristic
25C2×C11×C4⋊C4C2211yescharacteristic
26C2×C11×C4⋊C4C2211yescharacteristic
27C2×C11×C4⋊C4C2211yescharacteristic
28C2×C11×C4⋊C4C2211yescharacteristic
29C2×C11×C4⋊C4C2211yescharacteristic
30C2×C11×C4⋊C4C2211yescharacteristic
31C2×C11×C4⋊C4C2211yescharacteristic
32C2×C11×C4⋊C4C2211yescharacteristic
33C2×C11×C4⋊C4C2211yescharacteristic
34C2×C42×C11C2211yescharacteristic
35C2×C42×C11C2211yescharacteristic
36C2×C42×C11C2211yescharacteristic
37C2×C42×C11C2211yescharacteristic
38C2×C42×C11C2211yescharacteristic
39C11×#95C2211yescharacteristic
40C11×#95C2211yescharacteristic
41C11×#95C2211yescharacteristic
42C11×#95C2211yescharacteristic
43C11×#95C2211yescharacteristic
44C11×#95C2211yescharacteristic
45C11×#95C2211yescharacteristic
46C11×#95C2211yescharacteristic
47C11×#95C2211yescharacteristic
48C11×#95C2211yescharacteristic
49C11×#95C2211yescharacteristic
50C11×#95C2211yescharacteristic
51C11×#95C2211yescharacteristic
52C11×#95C2211yescharacteristic
53C2×Q8×C11—22no—
54C2×Q8×C11—22no—
55C2×Q8×C11—22no—
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C11×C4⋊C4—22no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4D414yes—
85C11×C4⋊C4Q814yescomplemented
86C42×C11—22no—
87C42×C11—22no—
88C42×C11—22no—
89C42×C11—22no—
90C42×C11—22no—
91#2462C1111yesmaximal, characteristic, direct product factor, Sylow
92C23×C11C2411yescharacteristic
93Q8×C11—28no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11C2×D412yes—
131C2×C4×C11C2×D412yes—
132C2×C4×C11C2×D412yes—
133C2×C4×C11C2×Q812yes—
134C2×C4×C11C2×Q812yes—
135C2×C4×C11C2×Q812yes—
136C2×C4×C11#4112yes—
137C2×C4×C11#4112yes—
138C2×C4×C11#4112yes—
139C2×#125C2×C1111yescharacteristic
140C2×C4×Q8C2×C1111yescharacteristic
141#398C2×C1111yescharacteristic
142#398C2×C1111yescharacteristic
143#395C2×C1111yescharacteristic
144#395C2×C1111yescharacteristic
145#389C2×C1111yescharacteristic
146#389C2×C1111yescharacteristic
147#387C2×C1111yescharacteristic
148#387C2×C1111yescharacteristic
149#387C2×C1111yescharacteristic
150#387C2×C1111yescharacteristic
151#387C2×C1111yescharacteristic
152#387C2×C1111yescharacteristic
153C4×C4⋊C4C2×C1111yescharacteristic
154C22×C11C22×D411yescharacteristic
155C22×C11C22×Q811yescharacteristic
156C22×C11C2×#4111yescharacteristic
157C22×C11C2×#4111yescharacteristic
158C22×C11C2×#4111yescharacteristic
159C22×C112−1+411yescharacteristic
160C22×C112−1+411yescharacteristic
161C4×C11—22no—
162C4×C11—22no—
163C4×C11—22no—
164C4×C11—22no—
165C4×C11—22no—
166C4×C11—22no—
167C4×C11—22no—
168C4×C11—22no—
169C4×C11—22no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176C22×Q8C22×C1111yescharacteristic
177#125—24no—
178C4×Q8—24no—
179C2×C4⋊C4C22×C1111yescharacteristic
180C2×C4⋊C4C22×C1111yescharacteristic
181C2×C4⋊C4C22×C1111yescharacteristic
182C2×C4⋊C4C22×C1111yescharacteristic
183C2×C4⋊C4C22×C1111yescharacteristic
184C2×C4⋊C4C22×C1111yescharacteristic
185C2×C4⋊C4C22×C1111yescharacteristic
186C2×C4⋊C4C22×C1111yescharacteristic
187C2×C4⋊C4C22×C1111yescharacteristic
188C2×C4⋊C4C22×C1111yescharacteristic
189C2×C4⋊C4C22×C1111yescharacteristic
190C2×C4⋊C4C22×C1111yescharacteristic
191C2×C4⋊C4C22×C1111yescharacteristic
192C2×C4⋊C4C22×C1111yescharacteristic
193C2×C4⋊C4C22×C1111yescharacteristic
194C2×C42C22×C1111yescharacteristic
195C2×C42C22×C1111yescharacteristic
196C2×C42C22×C1111yescharacteristic
197C2×C42C22×C1111yescharacteristic
198C2×C42C22×C1111yescharacteristic
199#95C22×C1111yescharacteristic
200#95C22×C1111yescharacteristic
201#95C22×C1111yescharacteristic
202#95C22×C1111yescharacteristic
203#95C22×C1111yescharacteristic
204#95C22×C1111yescharacteristic
205#95C22×C1111yescharacteristic
206#95C22×C1111yescharacteristic
207#95C22×C1111yescharacteristic
208#95C22×C1111yescharacteristic
209#95C22×C1111yescharacteristic
210#95C22×C1111yescharacteristic
211#95C22×C1111yescharacteristic
212#95C22×C1111yescharacteristic
213C2×C11#52511yescharacteristic
214C2×C11#53311yescharacteristic
215C2×C11#54111yescharacteristic
216C2×C11#54711yescharacteristic
217C2×C11D4×Q811yescharacteristic
218C2×C11#55211yescharacteristic
219C2×C11#55711yescharacteristic
220C2×Q8—22no—
221C2×Q8—22no—
222C2×Q8—22no—
223C22×C4C23×C1111yescharacteristic
224C22×C4C23×C1111yescharacteristic
225C22×C4C23×C1111yescharacteristic
226C22×C4C23×C1111yescharacteristic
227C22×C4C23×C1111yescharacteristic
228C22×C4C23×C1111yescharacteristic
229C22×C4C23×C1111yescharacteristic
230C22×C4C23×C1111yescharacteristic
231C22×C4C23×C1111yescharacteristic
232C22×C4C23×C1111yescharacteristic
233C22×C4C23×C1111yescharacteristic
234C22×C4C23×C1111yescharacteristic
235C22×C4C23×C1111yescharacteristic
236C22×C4C23×C1111yescharacteristic
237C22×C4C23×C1111yescharacteristic
238C4⋊C4—22no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4D4×C1114yes—
252C4⋊C4Q8×C1114yescomplemented
253C42—22no—
254C42—22no—
255C42—22no—
256C42—22no—
257C42—22no—
258C11#246211yescharacteristic, direct product factor, Sylow
259C23C24×C1111yescharacteristic
260Q8—28no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4C2×D4×C1112yes—
298C2×C4C2×D4×C1112yes—
299C2×C4C2×D4×C1112yes—
300C2×C4C2×Q8×C1112yes—
301C2×C4C2×Q8×C1112yes—
302C2×C4C2×Q8×C1112yes—
303C2×C4C11×#4112yes—
304C2×C4C11×#4112yes—
305C2×C4C11×#4112yes—
306C22C22×D4×C1111yescharacteristic
307C22C22×Q8×C1111yescharacteristic
308C22C2×C11×#4111yescharacteristic
309C22C2×C11×#4111yescharacteristic
310C22C2×C11×#4111yescharacteristic
311C22C11×2−1+411yescharacteristic
312C22C11×2−1+411yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—22no—
318C4—22no—
319C4—22no—
320C4—22no—
321C4—22no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C2C11×#52511yescharacteristic
329C2C11×#53311yescharacteristic
330C2C11×#54111yescharacteristic
331C2C11×#54711yescharacteristic
332C2D4×Q8×C1111yescharacteristic
333C2C11×#55211yescharacteristic
334C2C11×#55711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11C24
commutator, Frattini, cosocleC23C24×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
85. C11×C4⋊C4Q8semidirect
91. #2462C11direct (N × H)
252. C4⋊C4Q8×C11semidirect
258. C11#2462direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C11×#1252
C2×C4×Q8×C112
C11×#3982
C11×#3952
C11×#3892
C11×#3872
C4×C11×C4⋊C42
#246211